where \(\phi _N(t)\)  is the probability that the population gets from state \(i=1\)  to state \(i=N\)  after \(t\)  discrete steps. It should be clear from this definition that \(\sum _{t=0}^{\infty }\phi _N(t)=\rho _N\) . Following [1]}, we can obtain a recursive relation leading to the following expression (see [2]}, [3]} for alternative expressions):
\(t_N=\sum _{n=1}^{N-1}\dfrac{s_{0,n-1}s_{n,N-1}}{P_{n^+}^Nq_ns_{0,N-1}}, \hspace{12.0pt} s_{n,m}=\sum _{k=n}^{m}q_k, \hspace{12.0pt} q_n=\prod _{j=1}^{n}\gamma _j^N.\) 
